Answer: He run 7 high-speed intervals and 8 low-speed intervals.
Step-by-step explanation:
Let x = Number of high-speed intervals.
y= Number of low-speed intervals .
He runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds.
4 min 56 sec = (4(60)+56) sec = 296 sec [ 1 minute = 60 seconds]
According to the question , we have the following linear equations :
[tex]x+y=15\ ...(i)\\\\ 16x+23y=296\ ...(ii)[/tex]
Multiply (i)by 16 , we get
[tex]16x+16y=240\ ...(iii)[/tex]
Subtract (iii) from (ii)
[tex]7y=56\\\\\Rightarrow\ y=8[/tex]
Put value of y in (i) , we get
[tex]x+8=15\Rightarrow\ x=7[/tex]
Hence, he run 7 high-speed intervals and 8 low-speed intervals.
